Some inequalities for the growth of rational functions with prescribed poles

Let \mathcal R_{n} be the set of all rational functions of the type r(z) = f(z)/w(z), where f(z) is a polynomial of degree at most n and  w(z) = \prod_{j=۱}^{n}(z-\beta_j), |\beta_j|>۱ for ۱\leq j\leq n. In this paper, we prove some results concerning the growth of rational functions with prescribed poles by involving some of the coefficients of polynomial f(z). Our results not only improve the results of N. A. Rather et al. [۸], but also give the extension of some recent results concerning the growth of polynomials by Kumar and Milovanovic [۳] to the rational functions with prescribed poles and we obtain the analogous results for such rational functions with restricted zeros.

کلیدواژه ها:

Rational functions ، polynomials ، Inequalities